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An Annuity is a series of equal payments made at fixed intervals for a specified number of periods. These equal payments are denoted by the PMT and can occur at either the beginning or the end of each period. Future and Present Values of Annuity: Future Value of an Annuity can be calculated, where a series of equal payments are made at a fixed intervals for a specific number of periods. The principle applied here is just like Compounding. However, method of calculating Future Value of Annuity differs in Ordinary Annuity and Annuity Due. Similarly, Present Value of an Annuity can also be calculated by using the principle of Discounting, but the method of calculating Present Value of Annuity differs in Ordinary Annuity and Annuity Due. Types of Annuity: Annuity has following types depending on the period of payment.

1. Ordinary/Deferred Annuity:

If the payments of Annuity occur at the end of each period, it is called Ordinary or Deferred Annuity.

Future Value of Ordinary Annuity:

If equal payments PMT is made at the end of n periods, providing a saving of i, then Future Value of Annuity (FVa or FVAn) can be calculated as:

Present Value of Ordinary Annuity:

If equal payment PMT is made at the end of n periods, providing a saving of i, then Present Value of Annuity PVAn can be calculated as:

2. Annuity Due

If the payments of Annuity occur at the beginning of each period, such Annuity is called Annuity Due.

Future Value of Annuity Due:

If equal payment PMT is made at the beginning of n periods, providing a saving of i, then Future Value of such Annuity FVAn can be calculated as:

The only difference between Future Value of Deferred Annuity and Annuity Due is that every term of Future Value of Annuity Due is compounded for one extra period, reflecting the fact that each payment for an Annuity Due occurs one period earlier than Ordinary Annuity.

Present Value of Annuity Due:

If equal PMT is made at the beginning of n periods, providing a saving of i, then Present Value of such Annuity PVAn can be calculated as:

The only difference between Present Value of Deferred Annuity and Annuity Due is that every term of Present Value of Annuity Due is discounted for one extra period, reflecting the fact that each payment for an Annuity Due occurs one period earlier than for Ordinary Annuity.

3. Perpetuity

Some Annuities go on indefinitely, or perpetually, and are called Perpetuities. The Present Value of such Annuities is simple to calculate.

The process of going from today’s value (Present Value; denoted by PV) to Future Value (denoted by FV) is called Compounding. If i is the Interest Rate, then Interest Amount (INT) can be calculated as:

INT ($) = PV x i

The Future Value will be the Present Value plus the amount of Interest, so:

FV = PV + INT

FV = PV + PV x i

FV = PV (1 + i)

If the amount is deposited or invested for n periods, the same formula can be written as:

FVn = PVn (1 + i) n

The term (1 + i)n is known as Future Value Interest Factor and is denoted by FVIFi,n, so:

FVn = PVn (1 + i)n = PV (FVIFi,n)

In some cases, Interest is paid semiannually, which means Interest is paid twice a year. Similarly Interest payment 4 times a year means Interest is paid quarterly. For such cases, the above formula can be more generalized:

Where m is the number of times Interest Payment is made in a year. However, in such case, i is taken as Nominal Rate of Interest.

Discounting:

The process of calculating Present Value (PV) from Future Value (FV) is called Discounting. As we know:

FVn = PVn (1 + i) n

Solving for PV, we have:

Or we can write it as under:

PVn = FVn (1 + i)-n

The term (1 + i)-n is called Present Value Interest Factor, and is denoted by PVIFi,n; therefore:

PVn = FVn (1 + i)-n = FV (PVIFi,n)

Same as previous case, if the Interest is paid semiannually or quarterly, a more general formula is applicable:

Where i is taken as Nominal Rate of Interest.

Effective Annual Rate (EAR):

Effective Annual Rate is defined as the rate which would produce the same Future Value, if annual Compounding had been used. It is also called Equivalent Annual Rate, and can be calculated as:

As we have taken Annual Compounding, therefore n is not shown in the formula, and i will be taken as Nominal Rate of Interest.

When an investor invests in multiple
stocks/securities, it is called Investment Portfolio. Maintaining a Portfolio
is a very important step taken by investors. By maintaining a Portfolio, Risk
can be mitigated / minimized by maintaining a portfolio and higher margins of
profits can be earned. In this case, if one stock/security defaults, it does
not necessarily mean Investor is also in loss. Instead, investor can compensate
the loss of one stock from other stocks/securities. Fig. 5 shows how
maintaining a Portfolio minimizes the Portfolio Risk. Fig shows that Portfolio
size is taken on x-axis and portfolio risk on y-axis, which results a curved
graph.

Classification of Investors:

Investors can be classified on the basis of their risk-taking/bearing capacity. How much risk an investor bears, depends on investor’s personal capacity, attitude, interest and behavior. For example:

1. Risk Seekers

Risk seekers seek for riskier investment. They are capable of assuming a higher risk and have strong and healthy financial position.

2. Risk Avoiders

They avoid riskier investments, because they have not strong and healthy financial position. They choose those instruments, which have less variation in returns.

3. Risk Bearers

Risk bearers fall in between the above categories. They choose moderate levels of risk they can bear according to their capacity.

Hedging:

Risk reduction is known as Hedging. They do it by using Derivative Instruments.

Security:

A Security refers to a publicly traded financial instrument, as opposed to a privately placed instrument. Securities have greater liquidity than otherwise similar instruments, which are not traded in Open Market. Security is considered to be an insurance against an emergency, according to banking definitions.

Classification of Securities:

The securities have been classified according to the functional operation aspects as under:

1. Intangible Securities

These are personal exclusive undertakings by a party to pay the amount of advances outstanding against a borrower. Examples of such securities are Demand Promissory Note, bill of exchange or a Bond, Guarantee and Indemnity etc.

2. Tangible Securities

These are the securities which can be realized from sale or transfer. Examples of such securities are Shares, Stock, Land, Building and Goods.

3. Prime Securities

These are also called Primary Securities. Such securities are main covers for an advance and are deposited by the borrower himself. When a depositor of term deposits offers his Term Deposit Receipt to cover and advance, it is the Primary Security according to banking term.

4. Collateral Securities

These are the securities provided as an additional cover for an advance, where either he security is not very stable in value, or where the realization of the security to cover the outstanding amount of balance is difficult. In case of the default by borrower, bank has the authority to sell these shares of security and adjust the advance.

5. Movable Securities

These are the securities, which are legally and physically both in possession of the lending bank. Examples are Term Deposit Receipts, Goods, Vehicles and Merchandise etc.

6. Immovable Securities

These are the securities, where the legal possession or right to takeover is entrusted to the lending bank, but the physical possession remains with borrowers.

7. Government Securities

These are the long-term securities issued by the government for financing social programs. They are perceived as Risk-free, are highly liquid and carry attractive coupon rates. Like T-bills (Treasury Bills), government securities are sold through auctions and are actively traded in secondary markets.

Time Value of Money:

The theory of Time Value of Money states that the value of money decreases with the passage of time. This concept can be described as “A Dollar in hand today is more worth of a Dollar tomorrow”. This happens because of Inflation. Inflation is a situation, where the prices as a whole are increasing. The rate at which the prices are increase is known as Inflation Rate. Two terms are necessary to explain while discussing Inflation and theory of Time Value of Money:

1. Nominal Interest Rate/Quoted Interest Rate:

Nominal Interest Rate is a rate at which money invested grows. Banks generally offer Nominal Rate of Interest to the depositors.

2. Real Interest Rate

Real Interest is a rate, at which the purchasing power of an investment increases. Market Interest Rates are Nominal Interest Rates.

Relationship of Inflation, Nominal and Real Interest Rates:

Real Interest Rates, Nominal Interested Rates and Inflation Rates have strong relationship with each other, which can be expressed in the form of an equation:

Investment may be defined as an activity that commits funds in any financial/physical form in the present with an expectation of receiving additional return in the future. The expectation brings with it a probability that the quantum of return may vary from a minimum to maximum. This possibility of variation in the actual return is known as Investment Risk. Thus every investment involves a Return and Risk.

Investment is an activity that is undertaken by those who have Savings. Savings can be defined as the excess of Income over Expenditure. Two important characteristics of Investment are Return and Risk.

Return:

Every Investment has and expectation of Return, which is the margin earned by investor in future by investing at present. The margin earned reflects the concept of Time Value of Money, which describes that a Dollar currently held will be less worth tomorrow. Investors take advantage from this saving, which is called Return (denoted by kor r)

Risk:

Risk is the chance of uncertainty that may rise after investment. It is the event that may arise by affecting the Return of the Investment. Every investor should forecast the Return and Risk while investing and should keep into account all possible events that may occur in future. It is denoted by d and is the Standard Deviation, which reflects the deviation from the Expected Rate of Return.

The formulae for Risk and Return of and Investments are:

Relationship between Risk and Return:

Risk and Return have positive relation to each other (Direct Relationship):

Risk µ Return

The relationship shows that if an investment is tied with high expectation of Return, it will have high Risk and vice versa. This relationship is also shown in the diagram:

Types of Risk:

There are various types of Risk, among which, following are the most important to describe:

1. Business Risk:

Business Risk is one which is tied to a particular business. Such risk arises when the investor is not sure whether the business will successful or not in which he/she has invested.

2. Financial Risk:

Financial Risk is the additional risk placed on the common stockholders as a result of the decisions to finance with debt. The use of debt, also called Financial Leverage also concentrates the firm’s business risk on its stockholders. Financial Risk arises, when to decide whether the firm should be Levered (50% debt and a portion of equity) or Unlevered (All Equity). In this way, it makes the Capital Structure of a firm.

3. Country Risk:

Country Risk is one that arises from a particular country. A country’s environment may be favourable for investors, who want to invest in that country. Investors need to forecast such risk before making the investment decision.

4. Diversifiable Risk/Unsystematic/Idiosyncratic:

The part of a stock’s risk, that can be minimized/neglected is called Diversifiable Risk. Such Risk is caused by some random events like lawsuits, strikes, successful and unsuccessful marketing programs etc. This type of risk can be minimized while investing in multiple stocks; a phenomenon known as Diversification Principle.

5. Non-diversifiable/Systematic/Market Risk:

The part of stock’s risk, that cannot be minimized or neglected is known as Non-diversifiable Risk. This type of risk stems from factors that systematically affect most firms; such as war, inflation, recessions and high interest rates. Such risk remains constant even when investing in multiple stocks. It is measured in terms of Beta (β).

6. Inflation Risk:

Technically speaking, this type of risk is a subtype of Systematic Risk. This risk stems from variation in inflation rate. When inflation rate increases, it reduces the Real Interest Rate and vice versa. More detail about the relationship between Inflation Rate and Real Interest Rate will be explained in related articles.

7. Interest Rate Risk:

Interest Rate Risk can be said to be a subtype of Systematic Risk. This type of risk arises with the fluctuation on Interest Rate in market. The more is the market Interest Rate, the more will be Interest Rate Risk tied to a particular stock (will be explained in later articles).

8. Exchange Rate Risk:

Exchange Rate Risk stems from changes in Exchange Rate or currency fluctuations. The more is the currency fluctuation in market, the more will be the Exchange Rate Risk for and Investor.

9. Liquidity/Marketability Risk:

Liquidity Risks generally arise when one business acquires another business. Liquidity refers to a condition when a firm is not generating enough profit from its operations, that can meet the overall cost of a business. By doing so, investors of one organization purchase the stocks of Liquidating Firm, but are not sure whether their decision to purchase the stocks of such firm will benefit at a future date or not. Such uncertain factors are called Liquidity Risk, when combine together.

10. Political Risk:

Political Risk arise from the political environment of an economy. If a country’s political environment is uncertain and unfavourable, the investors are called facing Political Risk while investing in such country.

11. Stand-alone Risk:

If an investor has only one investment, the risk tied to that particular investment is known as Stand-alone Risk. If an investor has only one investment, it is highly risky for him/her, as he/she cannot compensate his/her loss from alternative stocks, in case the stock hald by him/her is losing its value.

12. Portfolio Risk:

If an investor has invested in multiple stocks/securities, the risk tied to all of those stocks/securities (combined together) is called Portfolio Risk. If a security defaults, the investor still has a chance to earn profit from other stocks/securities held by him/her. Portfolio Risk can be measured by the following formula.